Why is my cat vomiting, has diarrhea, and bloody stool but is active?

There are many things that could cause his symptoms. Unfortunately they are non-specific and could be a symptoms of almost anything. Bleeding from the anus frequently signifies a serious disorder. Possible causes of bleeding from the anus can include polyps or tumors of the colon or anus, abscess or infection of the anal gland, constipation, blood clotting disorders, autoimmune disease or even certain types of poisoning. Any chance he ate a toxic plant or was exposed to any toxins?

Intestinal parasites are another possibility. Whipworms are intestinal parasites. They are about 1/4-inch long and live in the cecum and colon of the cat, where they cause severe irritation to the lining of those organs. This results in watery, bloody diarrhea. They can also have weight loss and general debilitation. Whipworms are one of the most pathogenic (harmful) worms found in cats. Has a fecal sample been tested? Whipworms can also cause vomiting.

Any chance the blood is dripping from his penis and not the anus? In younger cats a common cause of bloody urine is the presence of crystals in urine (crystalluria). When left undiagnosed and untreated, these crystals can lead to blockage of the urethra in some male cats. Has a urinalysis been done?

This is the best I can tell you at this time. If you have more detailed questions or want to speak one on one you can also opt to do a private consultation with me. Hope this helps. Best wishes.